Question

use the quadratic formula to solve the equation. 8m² + 2m = 5 m = (type an exact answer, using radicals as needed. use a comma to separ

Explanation:

Step1: Rewrite to standard quadratic form

$8m^2 + 2m - 5 = 0$

Step2: Identify a, b, c values

$a=8,\ b=2,\ c=-5$

Step3: Substitute into quadratic formula

The quadratic formula is $m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Substituting values:
$$m=\frac{-2\pm\sqrt{2^2-4(8)(-5)}}{2(8)}$$

Step4: Calculate discriminant

$\sqrt{4 + 160}=\sqrt{164}=\sqrt{4\times41}=2\sqrt{41}$

Step5: Simplify the expression

$$m=\frac{-2\pm2\sqrt{41}}{16}=\frac{-1\pm\sqrt{41}}{8}$$

Answer:

$m=\frac{-1+\sqrt{41}}{8},\ \frac{-1-\sqrt{41}}{8}$